Basic Math Examples

$\frac{(2 n^{\frac{1}{3}}) (3 n^{\frac{1}{3}} - 4 n^{\frac{4}{3}})}{2 n^{- \frac{1}{3}}}$

Step 1

Move $n^{- \frac{1}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{(2 n^{\frac{1}{3}}) (3 n^{\frac{1}{3}} - 4 n^{\frac{4}{3}}) n^{\frac{1}{3}}}{2}$

Step 2

Multiply $n^{\frac{1}{3}}$ by $n^{\frac{1}{3}}$ by adding the exponents.

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Step 2.1

Move $n^{\frac{1}{3}}$ .

$\frac{2 (n^{\frac{1}{3}} n^{\frac{1}{3}}) (3 n^{\frac{1}{3}} - 4 n^{\frac{4}{3}})}{2}$

Step 2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2 n^{\frac{1}{3} + \frac{1}{3}} (3 n^{\frac{1}{3}} - 4 n^{\frac{4}{3}})}{2}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{2 n^{\frac{1 + 1}{3}} (3 n^{\frac{1}{3}} - 4 n^{\frac{4}{3}})}{2}$

Step 2.4

Add $1$ and $1$ .

$\frac{2 n^{\frac{2}{3}} (3 n^{\frac{1}{3}} - 4 n^{\frac{4}{3}})}{2}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor.

$\frac{2 n^{\frac{2}{3}} (3 n^{\frac{1}{3}} - 4 n^{\frac{4}{3}})}{2}$

Step 3.2

Divide $n^{\frac{2}{3}} (3 n^{\frac{1}{3}} - 4 n^{\frac{4}{3}})$ by $1$ .

$n^{\frac{2}{3}} (3 n^{\frac{1}{3}} - 4 n^{\frac{4}{3}})$

Step 3.3

Apply the distributive property.

$n^{\frac{2}{3}} (3 n^{\frac{1}{3}}) + n^{\frac{2}{3}} (- 4 n^{\frac{4}{3}})$

Step 3.4

Reorder.

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Step 3.4.1

Rewrite using the commutative property of multiplication.

$3 n^{\frac{2}{3}} n^{\frac{1}{3}} + n^{\frac{2}{3}} (- 4 n^{\frac{4}{3}})$

Step 3.4.2

Rewrite using the commutative property of multiplication.

$3 n^{\frac{2}{3}} n^{\frac{1}{3}} - 4 n^{\frac{2}{3}} n^{\frac{4}{3}}$

Step 4

Simplify each term.

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Step 4.1

Multiply $n^{\frac{2}{3}}$ by $n^{\frac{1}{3}}$ by adding the exponents.

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Step 4.1.1

Move $n^{\frac{1}{3}}$ .

$3 (n^{\frac{1}{3}} n^{\frac{2}{3}}) - 4 n^{\frac{2}{3}} n^{\frac{4}{3}}$

Step 4.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 n^{\frac{1}{3} + \frac{2}{3}} - 4 n^{\frac{2}{3}} n^{\frac{4}{3}}$

Step 4.1.3

Combine the numerators over the common denominator.

$3 n^{\frac{1 + 2}{3}} - 4 n^{\frac{2}{3}} n^{\frac{4}{3}}$

Step 4.1.4

Add $1$ and $2$ .

$3 n^{\frac{3}{3}} - 4 n^{\frac{2}{3}} n^{\frac{4}{3}}$

Step 4.1.5

Divide $3$ by $3$ .

$3 n^{1} - 4 n^{\frac{2}{3}} n^{\frac{4}{3}}$

Step 4.2

Simplify $3 n^{1}$ .

$3 n - 4 n^{\frac{2}{3}} n^{\frac{4}{3}}$

Step 4.3

Multiply $n^{\frac{2}{3}}$ by $n^{\frac{4}{3}}$ by adding the exponents.

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Step 4.3.1

Move $n^{\frac{4}{3}}$ .

$3 n - 4 (n^{\frac{4}{3}} n^{\frac{2}{3}})$

Step 4.3.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 n - 4 n^{\frac{4}{3} + \frac{2}{3}}$

Step 4.3.3

Combine the numerators over the common denominator.

$3 n - 4 n^{\frac{4 + 2}{3}}$

Step 4.3.4

Add $4$ and $2$ .

$3 n - 4 n^{\frac{6}{3}}$

Step 4.3.5

Divide $6$ by $3$ .

$3 n - 4 n^{2}$